This example outlines an aplication of the Maple + GrTensorII enviroment
for the canonical treatment of the general relativity (ADM formalism) based
on the 3+1 split of spacetime. There are two version of the program below
. The first one is devoted to the "pure" ADM formalism, using the notations
and conventions as they are described in "*Gravitation"* by Wheeler,
Misner Thorne (Freeman, 1973) in chapter 21, pg. 484 (**canonical.mws
**and **biaI_din.mpl)**. The program is adapted to the Bianchi I space
time but can be easily modified for other examples. It produces the constraints
equations (the hamiltonian one and the momentum constraitns) and the dymanical
equations for the three dimensional metric and for the three dimensional
momenta components. A version of the ADM reductional formalism is developed
- this part is strongly depending on the symmetry of the space-time. The
second worksheet (**Desitter.mws** and **desitter_sf.mpl**) is a
modified form of the first one to the ADM formalism widely used in
numerical relativity. Here instead of the momenta canonical conjugated
to the three dimensional metric we used the components of the extrinsic
curvature. We included also the minimal interaction of a scalar field with
gravitation. Both programs can be used in various topics from gravity theory,
as hamiltonian or inflationary cosmology, and of course in generating initial
data for numerical relativity.

- Related papers (containing more informations) :
- Canonical mws || html
- Desitter mws || html
- Dowload the metric files biaI_din.mpl and desitter_sf.mpl

These will appear on the right. Highlite and save these in your metrics directory for GRTensorII.